Computerized process control system for the growth of synthetic quartz crystals

ABSTRACT

A computer-controlled, hydrothermal, crystal-growing process, for example, for growing synthetic quartz crystals of uniformly high Q. The disclosure includes a mathematical model of the crystal-growing autoclave and an algorithm by which a digital, process-control computer can make adaptive changes to the currents supplied to heating elements associated with the upper and lower zones of the autoclave, during the 25 day growth cycle, to yield a superior crystal of high Q.

sauna EX ,1 XW777 ill- XR a a i A d, t ig BEST AVAILABLE COPY United in... [111- 3,805,044 1 Bhattacharyya et a1. Q E- E Apr. 16, 1974 [54] COMPUTERIZED PROCESS CONTROL 3,621,213 11/1971 Jen et a1. 235/150 SYSTEM FOR THE GROWTH OF SYNTHETIC QUARTZ CRYSTALS [75] Inventors: Ranendra K. Bhattacharyya,

Kendall Park, N.J.; Angelo Ralph Primary Examiner-Eugene G. Botz Attorney, Agent, or Firm-W. M. Kain; R. P. Miller; R.

C. W' Flore, Jr., Westville; David William Rudd, E. Derry, both of NH.

[73] Assignee: Western Electric Company Incorporated, New York, NY. [57] ABSTRACT [22] Filed: Apr. 7, 1971 A computer-controlled, hydrothermal, crystal-growing I [21] Appl 131916 process, for example, for growing synthetic quartz crystals of uniformly high Q. The disclosure includes [52] US. Cl. 235/l5l.l2, 23/301 R atical model of the crystal-growing auto e [51] Int. Cl. G06f 15/46 n n algorithm y which a g p nt [58] Field of Search 235/1511, 151.12; computer can make adaptive changes to the currents 23/301 R supplied to heating elements associated with the upper and lower zones of the autoclave, during the 25 day [56] References Cited growth cycle, to yield a superior crystal of high Q.

UNITED STATES PATENTS 3,183,063 5/1965 Gilson et a1 23/301 R 25 Claims, 25 Drawing Figures INPUT CONVERTER r39 DEVICE :51 r 1 PR 1: cozii oi cg i' c ii CENTRAL our ur INPUT PROCESS'NG 141/ cmcun cmcun UNIT 0 1 L I57 L 158 :42 y OUTPUT CONVERTER CONTROL DEV CE I53 cmcun r44 154 CLQCK cmcuar A/D couvzmza BEST AVAILABLE COPY PATENTEUAPR 15 mm SHEET 010F16 A ENT'U S TT ZJ CRYSTAL GROWTH PATENTEDAFR l 6 I974 sum "oznr 1e I60 TH IOO CRYSTAL GROWTH RATE IN MlLS/DAY IO' I5 20 25 ELAPSED TIME IN .DAYS

CRYSTAL GROWTH AND GROWTH RATE VERSUS ELAPSED TIME I 1 l 5 l0 I5 20 25 3Q ELAPSED TIME IN DAYS CRYSTAL Q AS A FUNCTION OF GROWING TIME TE MPERATURE BEST AVAILABLE COPY PATENTEDAPR I6 I974 3.8051344 saw our 16 TLgLE LOWER Z I I I I I I I o IO I5 20 3o ELAPSED TIME IN DAYS AND LOWER AUTOCLAVE TEMPERTURE ER VS. TIME ZONE T I I I I -I5 40 -5 o 4 5 IO l5 TIME IN MINUTES AUTOCORRELATION OF STEADY STATE REGIONS BEST AVAILABLE COPY PATENTED APR I 5 I974 3 8 O5 O44 sum '0SUF16 R MS ERROR I I I I I O I 2 3 4 5 ELAPSED TIME IN HOURS R.M.S. ERROR VS. TIME yjIIN Ma. x MINUTE) ESTIMATED VALUE OF PARAMETER W AS A FUNCTION OF 6 (REGION FOUR OF UPPER ZONE) BEST AVAILABLE COPY PATENTEDAPR 16 I974 3805L044 SIII'IU 06Uf16 II |oOoa REGION IREOlON I REGION 3 800 2 3 E E 600- 2 R E 400- I I i I 1 O 5 IO I5 20 25 ELAPSED TIME (IN HOURS) TEMPERATURE OF UPPER 8 LOWER AUTOCLAVE ZONES DURING WARM-UP PHASE A,, 2 ZuNT I. yI|+ +l)- ][y(|+ ){I }+B.INT. U(l+jK)- K] AUTOCLAVE TEMPERATURE-PREDICTING FORMULA T" g- 2 3 INT =v V 2+A.lNT 2 v ""I I BINT HEATER CURRENT CALCULATING FORMULAE I 33 F? g; J3

FORMULAE TO UPDATE PARAMETER K PATENTED AFR I 6 I974 BEST AVAILABLE COPY sum 09 or 16 DEFINE: INT, R, DELT, NOBS, s1, s2, s3, NB, NT,BDATA (6) AND TDATAIC) ENTER FORMULA USED TO PREDICT TEMPERATURE (SEE FIG.III

ENTER FORMULAE USED TO COMPUTE HEATER cuRRENT (SEE FIG. :2)

ENTER FORMULAE USED TO UPDATE PARAMETER K (SEE FIG.|3I

ENTER ESTIMATED OFF-LINE PARAMETERS FOR UPPER AND LOWER AUTOCLAVE ZONES FOR THREE WARM- UP AND ONE RUN REGION (SEE FIG.I4I

INITIALIZE VALUES OF MI M2 M3 SET i=I, AND

BX(I)=O, TXII)=O [READ VALUE OF BVII) I PATENTEDAPR I 5 am SET NFLAG I BEST AVAILABLE COPY saw 10 or 16 SET SET NFLAG 2 NFLAG 3 I I I READ VALUES OF BV(i) AND TVIiI SET BXIII AT ITS MAXIMUM VALUE READ B u i 4 AND am SET KA= N B, 1 AND y (i) 8 v SET NFLAG=4 CALL ESTIMATED OFF LINE PARAMETERS CORRESPONDING TO NFLAG (FIG.I4)

FOR MULAE UPDATE K USING UPDATING (FIG.I3) WITH COMPUTE TEMPERATURE OF LOWER ZONE USING TEMPERA- TURE PREDICTING FORMULAE (FIG.II) WITH 8% COMPUTE A Mi +1 H y (i +j+ I) DELT PATENTEDAPR 161974 BEST AVALABLE CC PY 7 3805044 sum 11 or 16 l I i SET SET

Ml M +l YES SET NFLAG 2 SET SET =1 K=NT PATENTEBAPR 1 6 1974 8537 AILABLE Copy 3.805044 saw 12 9F 16 CALL ESTIMATED OFF-LINE PARAMETERS CORRESPONDTNG TO (NFLAG 4) UPDATE K USING UPDAT- ING FORMULA (FIG- l3) WITH V=TV AND/ 13a COMPUTE DESIRED TEMPERATURES FOR UPPER ZONE USING TEMPERA TURE PREDICTING FORMULAE (FIG. H) W|TH/ =T/ SET YES CALL FORMULAE USED TO COMPUTE HEATER CURRENTS (FIGTIZ) COMPUTE HEATER CURRENT 'X. (i)

PATENTED 15 i974 EEST AVAILABLE COPY 3805;044

sum 13 or 16 FEED HEATER CURRENT TO UPPER ZONE OF AUTOCLAVE SET i i I YES SET

BVH) TBV (i V TV(i)= TTV (i) B/*(i)= TB/- (5) mun w, (a)

YES

SET

@ sr AVAILABLE COPY PATENTEDAPR 16 m4 saw 1n HF 16 SET M3= M3+ I YES NFLAG=4 CALL ESTIMATED OFF-LINE PARAMETERS CORRESPOND- ING TO NFLAG (FIG. l4)

COMPUTE 1 gl l CALL FORMULA USED TO COMPUTE HEATER CURRENT (SEE F|G.I2)

COMPUTE HEATER CURRENT 'X(i) AND FEED TO LOWER ZONE HEATERS CALL FORMULA USED TO UPDATE PARAMETER K WITH V= B V AND A a,

9&8? AVAILABLE (IOPY ATENTEDAPR 16 mm 35305044 sum 16 or 16 X] (IN Mo. X MINUTE) REGION FOUR OF LOWER ZONE I I I -o.o5

REGION ONE OF UPPER ZONE COMPUTERIZED PROCESS CONTROL SYSTEM FOR THE GROWTH OF SYNTHETIC QUARTZ CRYSTALS BACKGROUND OF THE INVENTION 1. Field of the Invention Broadly speaking, this invention relates to the growth of synthetic crystals. More particularly, in a preferred embodiment, this invention relates to a computercontrolled process for growing synthetic crystals having substantially uniform mechanical properties throughout all crystallographic regions of the crystal.

2. Discussion of the Prior Art In 1880, Pierre and Jacques Curie discovered that when mechanical stress was applied to opposite faces of a natural crystal, such as Rochelle Salt, an electric potential was developed across some other pair of faces. They also discovered that the application of an electric potential to opposite faces of the crystal resulted in mechanical strain, and a change in dimensions, between two other opposite faces of the crystal.

This phenomenon is called piezoelectricity and was regarded as little more than a scientific curiosity until the l930s, when it was realized that the inherent mechanical resonance of a piezoelectric crystal could be utilized to control the frequency of an electronic oscillator, or to improve the band-pass characteristics of a tuned audio-frequency, or radio-frequency filter.

Of the many known crystals exhibiting this phenomenon, silicon dioxide, or quartz, has proved to be most suitable for use in electronic circuitry. This is due to the superior physical properties possessed by quartz, for

example, high mechanical strength and good stability at temperatures in excess of 100C.

An important factor in analyzing the performance of a vibrating piezoelectric crystal is its internal friction. This parameter may be defined as the ratio of the energy which is converted into heat within the crystal to the total energy supplied to the crystal when resonating at its natural frequency. Clearly, the internal friction is related to imperfections in the crystal structure. Because this energy loss is low, the numerical value for the internal friction of mostcrystals is a very small number. It is, thus, more convenient to define a quality factor, Q, equal to the reciprocal of the internal friction. This mechanical Q is analogous to the Q of a tuned L,R,C circuit defined as Q (wL/R) (l/mCR) where w Zrr X the frequency of resonance.

The excellent circuit properties of uartz are due, in part, to the very high ratio of mass to elastance (this is equivalent to a high L/C ratio in a conventional tuned circuit) and to the very high ratio of mass to damping (this is equivalent to a high Q in a conventional tuned circuits). The Q of a natural quartz crystal is in the order of from 10,000 to 30,000 with values ranging up to 500,000 or more for specially treated crystals mounted in a vacuum.

The telephone industry is the largest single user of quartz crystals. These crystals are employed, for example, in the channel filters associated with frequency multiplex carrier systems, and as frequency control elements in the oscillators associated with coaxial cable carrier systems, and the like.

As the demand for telecommunications channels continues to increase, the telephone industry has been BEST AVAILABLE COPY forced to use carrier systems having carrier frequencies and sidebands which fall higher and higher in the frequency spectrum. Over the last few decades, there has, thus, been a corresponding increase in the Q requirements for crystal control elements. For example, the Q requirements of a typical quartz resonator have been found to be as follows: from 0 to Khz a Q of about l00,000 is required; from 100 to 300 Khz a Q of about 300,000 is required; from 300 Khz to about I Mhz a Q of from 400,000 to 800,000 is required; and from 1 to 10 Mhz crystals having Qs up to 1,000,000 are required.

Silicon dioxide, or natural quartz, is believed to constitute approximately 1/10 of the earth's crust. Al-

though large deposits of low quality quartz are found in the United States and in Madagascar, this low quality quartz is of no direct use for the critical requirements of the electronic and telecommunication industries. Large crystals, of a quality sufficiently high for telecommunications use, are found only in Brazil. Although, in processed form, quite literally worth more than their weight in gold, Brazilian quartz is obtained, not from any organized mining operation, but rather from entrepreneurs who dig the crystals from the ground or find them in the beds of rivers. Obviously, this is a very unstable source of supply and requires the maintenance of large and expensive stockpiles. In any event, the supply of natural quartz crystals, of appropriate size and quality, is no longer capable of fulfilling the demands of the electronics and telecommunication industries.

Attempts to grow synthetic piezoelectric crystals date back well over 100 years, but because piezoelectricity itself was little more than a laboratory phenomenon, and there was no economic incentive, these attempts were generally unsuccessful. It was not until World War II that any serious effort was undertaken to find a way to create synthetic piezoelectric crystals of useful size and Q.

ln the United States, the use of the synthetic piezoelectric material EDT (ethylene diamine tartrate) was considered, but artificial crystals of EDT did not prove entirely satisfactory as the very solubility of the crystals contributing to the ease with which they could be artificially grown, was a handicap during the processing of the crystals, as was their fragility. Also, EDT crystals were electronically inferior to natural quartz.

After World War II, a review of captured documents revealed that Gennan scientists had achieved some success in growing synthetic quartz crystals using a hydrothermal technique with silica as the nutrient. The results of these experiments, however, were unpredictable and continuity was not achieved; only a porous mass of fine quartz needles resulted and these fine needles were, of course, totally unsuited for any commercial electronic application.

Spurred on by the German research, and foreseeing a shortage of natural quartz in the years to come, scientists in the United States continued research into the problem of growing synthetic piezoelectric crystals, of reasonable size and O, which would be suitable for use in electronic applications.

United States Pat. No. 2,785,058, which issued on Mar. 12, 1957 in the name of E. Buehler, and which is assigned to a subsidiary of the assignee of the instant invention, disclosed the first really practical method of growing synthetic quartz crystals suitable for electronic BEST AVAILABLE COPY use. As disclosed in that patent, along cylindrical autoclave is divided by a baffle plate into an upper zone, called the crystallization zone, and a lower zone, called the dissolving zone. The lower, or dissolving zone, comprises about one half the total volume of the autoclave and is filled with small pieces of natural quartz, referred to as the nutrient. In the upper. or crystallization zone, small plates of quartz, of known orientation, called the seed crystals, are suspended from a rack. The remaining volume of the autoclave is filled to about 80 percent capacity with a solvent which is capable of dissolving quartz. for example, a week aqueous, alkaline solution of sodium hydroxide (NaOl-I). As discussed in US. Pat. No. 3,356,463, dopants, such as lithium nitrate (LiNO may be added to the solution to improve the characteristics of the crystals. The vessel is then sealed and heat is applied to the upper and lower zones of the autoclave. Typically, the upper zone is heated to about 630F and the lower zone to about 700F. The action of the heat causes the nutrient quartz to dissolve in the alkaline solution and, because the upper zone is relatively cooler than the lower zone, the solvated quartz flows by convection to the upper end of the autoclave. The baffle plate which separates the two halves of the autoclave contains a plurality of small holes, and serves to maintain two essentially isothermal zones within the vessel. In addition, the baffle plate helps to channel the convected flow of solvated quartz from the lower zone to the upper zone. The action of the heat which is applied to the autoclave causes the aqueous solution of a sodium hydroxide within the autoclave to expand, generating pressures in the order of 25,000 pounds per square inch. Because the upper, or crystallization zone, is some 70F cooler than the lower zone, when the aqueous solution arrives at the upper zone, it cools and quartz precipitates out of solution and nucleates onto the seed crystals in the form of a single crystal. The process varies in time, depending upon the size of the crystals desired, but nominal growing times are in the order of from three to four weeks.

It has been observed that the Q of crystals grown by the process described in U. S. Pat. No. 2,785,058, varies throughout all crystallographic regions of the crystal. This has been attributed to impurities in the crystal which are segregated in response to variations in growth rate during the growth process. These variations in growth rate are believed to be a consequence of the design of the autoclave and its relation to the growing crystal, in addition to the natural anisotropy of the crystal. For example, during the first few days of synthesis, the size of the crystal is not sufficiently large to inhibit the convective flow of solvated quartz from the lower zone of the autoclave to the upper zone of the autoclave. The crystals, therefore, grow at a rapid rate. This effect, however, decreases with time, because as the crystals grow, they occupy an increasingly larger portion of the upper autoclave zone, thereby inhibiting the convective flow of solvated quartz, and reducing the rate of crystal growth. The decrease in growth rate leads, in turn, to a rejection of impurities, with a subsequent enhancement of the crystal Q. Thus, the Q of the crystal in the vicinity of the seed is lower than the Q at the extremities of the crystal.

In the above-described process, the seed crystals grow in X, Y, and Z directions. However, because of the crystallographic orientation of the seed crystal, and the physical arrangement within the autoclave, by far the greatest amount of growth occurs in the Z direction. For this reason, the above-described crystal growing process is referred to as a fast Z-growth, or fast basal growth process. 5 At the end of the growth cycle, the synthetic crystals are removed from the autoclave for further processing. Crystal units are then cut from the synthetic crystals and, as is well known, these cuts may be made in any of several orientations, for example, X cut, Y cut, BT cut, CT cut, etc. For telecommunication purposes, however, most quartz crystal devices operate in the lower and middle frequency ranges. Thus, the majority of crystal cuts are made in the basal plane, parallel to the seed crystal. Unfortunately, the Z growth plane is particularly susceptible to impurity segregation and, as previously discussed, these impurities tend to decrease the value of the crystal Q by increasing the internal friction of the crystal. Thus, crystal units which are cut from slices parallel to the seed crystal are more likely to have larger Q variations than crystal units which are cut from slices making an angle with the seed.

As previously mentioned, because the rate of crystal growth falls continuously during the growth cycle, the number of impurities which succeed in attaching themselves to the crystal also falls, thus, steadily raising the Q of the crystal in the direction of the crystal surfaces. Accordingly, the Q of a basal cut slice will vary throughout the slice and the average Q, from slice to slice, will also vary.

The actual difference in Q between a basal cut slice taken close to the seed and one taken close to the Z surface is considerable. For example, a slice taken close to the seed may have a Q of only 120,000, whereas a slice cut from near the outer Z surface of the same crystal may have a Q of as high as 260,000, more than a 2:1 ratio. Clearly, this is a most undesirable situation, for if the Q of the near slice is considered to be the limiting factor, then slices taken further from the seed will have a Q far in excess of the requirements of the circuit with which they are intended to operate, resulting in wasteful economic loss. On the other hand, if the Q of slices taken some distance from the seed crystal is considered to be the limiting factor, then the entire portion of the crystal which is close to the seed must be scrapped, resulting again, in wasteful economic loss.

The problem, then, is to find a technique for growing synthetic crystals whereby the crystals may be made to exhibit predetermined mechanical properties throughout selected crystallographic regions thereof.

This problem has been solved by the instant invention, in which, a substantially vertically disposed autoclave is charged with a crystal growing nutrient, the autoclave being functionally divided into two essentially isothermal zones. The autoclave is then partially filled with a solvent capable of dissolving said nutrient, and at least one seed crystal suspended, proximate the upper zone of the autoclave. The autoclave then is sealed and heat is applied to the upper and lower zones thereof to increase the pressure and temperature above the levels required to dissolve the nutrient in the solvent. The temperature of the lower zone is established at a higher value than that of the upper zone to permit a convective flow of solvated nutrient over the surfaces of the seed crystal. Thereafter, the temperature differential between the upper and lower zones is altered selectively as time proceeds so as to change t e tale 0f BEST AVAILABLE COPY flow of solvated nutrient over the seed crystal. In this fashion, the growth rate of the crystal is selectively altered thereby causing the crystal to exhibit the desired predetermined mechanical properties.

One illustrative apparatus for practicing the above method comprises a substantially vertically disposed autoclave which is functionally divided into an upper and a lower zone. The autoclave is adapted to receive a charge of crystal growing nutrient in the lower zone and of being substantially filled with a solvent capable of dissolving the nutrient. The apparatus further includes means for suspending at least one seed crystal within the autoclave, proximate the upper zone thereof as well as first and second heating means which are respectively associated with the upper and lower zones.

A source of energy for the first and second heating means is also provided as well as computer means for respectively adjusting the amount of energy supplied to the first and second heating means from said source, whereby the temperature differential between the upper and lower zones of the autoclave is selectively altered during the crystal growing process.

The invention, and its mode of operation, will be more fully understood by reference to the following detailed description and to the drawings, in which:

DESCRIPTION OF THE DRAWINGS FIG. 1 is a partially cut-away, isometric view of an hydrothermal autoclave of a type suitable for use with the present invention;

FIG. 2 is a graph depicting the relationship between crystal growth and growth rate, as a function of time, for a crystal grown in the autoclave of FIG. 1;

FIG. 3 is a graph depicting the relationship between the Q of a crystal and the elapsed time for a crystal grown in the autoclave of FIG. 1;

FIG. 4 is a drawing, prepared from an actual photography of a shadowgram, showing how the Q of a crystal is assigned to different physical locations within the body of the crystal;

FIG. 5 is a graph depicting the relationship between the Q of a crystal and its growth rate for a crystal grown in the autoclave of FIG. 1;

FIG. 6 depicts an illustrative profile of the desired temperatures for the upper and lower zones of a computer-controlled autoclave according to the present invention;

FIG. 7 is a graph which depicts the autocorrelation between samples in the mathematical model of the autoclave of the present invention;

FIG. 8 is a graph depicting the root mean square error, as a function of time, for the mathematical model of the autoclave of the present invention;

FIG. 9 depicts a graph of the estimated value of the parameter w, as a function of y, for region 4 of the upper zone in the mathematical model of the autoclave of the present invention;

FIG. 10 is a graph depicting the relationship between the upper and lower zone temperatures, as a function of time, during the warm-up phase of the autoclave of FIG. 1;

FIG. 11 depicts the formula used to predict the temperature of the autoclave of FIG. 1;

FIG. 12 depicts the formulae used to compute the heater currents for the heating elements associated with the autoclave of FIG. 1;

FIG. 13 depicts the formulae used to update the value of the parameter K in the mathematical model of the autoclave of FIG. 1;

FIG. 14 depicts the values of the estimated off-line parameters for the mathematical model of an experimental hydrothermal autoclave actually built and tested;

FIG. 15 depicts one illustrative apparatus configuration for practicing the present invention;

FIGS. 16 22 depict an illustrative logical flow chart for implementing the algorithm of the present invention;

FIG. 23 illustrates the manner in which FIGS. 16 22 should be assembled;

FIG. 24 depicts a graph of the estimated value of the parameter w, as a function of 7, for region 4 of the lower zone in the mathematical model of the autoclave of FIG. 1; and

FIG. 25 depicts a graph of the estimated value of the parameter w, as a function of y, for region 1 of the upper zone in the mathematical model of the autoclave of FIG. 1.

DETAILED DESCRIPTION OF THE INVENTION This invention is based upon the discovery that the uniformity of synthetically-grown crystals may be improved by controllably increasing the temperature differential between the upper and lower zones of an autoclave, throughout the growth cycle, to maintain a relatively constant rate of flow of solvated nutrient over the seed crystals.

The effect of increasing the temperature differential between the upper and lower zones of the autoclave, considered by itself, is to increase the rate of flow of solvated nutrient over the seed crystals. However, as previously noted, as the crystals expand they fill an ever-increasing proportion of the autoclave. Thus, there is a tendency for the rate of flow of solvated nutrient to steadily decrease with time. By carefully adjusting the temperature differential as a function of time, these two effects can be balanced, one against the other, so that the net effect is a relatively constant flow of solvated nutrient over the seed crystals, throughout the entire growth cycle.

Implementation of the above-described technique, however, is by no means a simple matter. First, the crystal growing process must be mathematically characterized so that the temperature differential necessary to maintain a constant rate of convective flow can be calculated for any instant of time during the growth cycle. Next, a real-time, direct digital control algorithm must be derived so that appropriate changes may be made to the current which is supplied to the heating coils associated with the upper and lower zones of the autoclave to produce the desired temperature differential for the time period of interest.

The illustrative embodiment of the invention, to be discussed below, pertains to the growth of synthetic quartz crystals. One skilled in the art, however, will appreciate that the invention is not so limited, and may be used with equal facility in any hydrothermal crystal growing process. The use of the invention to grow crystals other than quartz merely requires modification of the parameters of the control algorithm and the crystal growing equations.

Before discussing, in detail, the mathematical characterization of the crystal growing process and the con- 

1. A hydrothermal method for growing synthetic crystals which exhibit predetermined mechanical properties, comprising the steps of: charging a substantially vertically disposed autoclave with a crystal growing nutrient, said autoclave being functionally divided into two, essentially isothermal, zones; partially filling said autoclave with a solvent capable of dissolving said nutrient; suspending at least one seed crystal in said autocalve, proximate the upper zone thereof; sealing said autoclave to form a totally enclosed member including therein said nutrient, said solvent and said at least one seed crystal; applying heat to the upper and lower zones of said autoclave to increase the pressure and temperature therein above the levels necessary to cause said nutrient to dissolve in said solvent, the application of said heat being such that the temperature of the lower zone is higher than the temperature of the upper zone so that a convective flow of solvated nutrient is established over the surfaces of said seed crystal; and selectively altering the temperature differential between the upper and lower zones of said autoclave, as time proceeds, to change the rate of flow of solvated nutrient over said at least one seed crystal; whereby the growth rate of said crystal is selectively altered and said crystal caused to exhibit said predetermined mechanical properties.
 2. The method according to claim 1 wherein said heat applying step comprises: passing a first electrical current through at least one electrical heater disposed about the upper zone of said autoclave; and passing a second electrical current through at least one electrical heater disposed about the lower zone of said autoclave.
 3. The method according to claim 2 wherein said selective temperature altering step comprises: varying the current supplied to at least one of said electrical heaters according to an empirically derived equation descriptive of the manner in which the temperatures of the upper and lower zones of the autoclave change, as a function of a change in the corresponding heater current, the equation being of the form d/dt ( y(t + Tau )) + Ay(t + Tau ) Bx(t) + C + N where, y(t + Tau ) the temperature of the corresponding zone at the instant t + Tau ; Tau the transport delay; N The stochastic noise term; A the time constant of the system; B/A the steady-state differential gain; and C/A the steady-state temperature of the corresponding autoclave zone when the heater current supplied thereto is zero.
 4. The method according to claim 1 wherein said synthetic crystal comprises quartz.
 5. A hydrothermal method for growing synthetic crystals which exhibit substantially uniform mechanical properties throughout all crystallographic regions of the crystal, comprising the steps of: charging a substantially vertically-disposed autoclave with a crystal growing nutrient, said autoclave being functionally divided into two essentially isothermal zones; partially filling said autoclave with a solvent capable of dissolving said nutrient; suspending at least one seed crystal in said autoclave proximate the upper zone thereof; sealing said autoclave to form a totally enclosed member including therein said nutrient, said solvent and said at least one seed crystal; applying heat to the upper and lower zones of said autoclave to increase the pressure and temperature therein above the levels necessary to cause said nutrient to dissolve in said solvent, the application of said heat being such that the temperature of the lower zone is higher than the temperature of the upper zone so that a convective flow of solvated nutrient is established over the surfaces of said seed crystal; and selectively increasing the temperature differential between the upper and lower zones of the autoclave, as time proceeds, to offset the natural tendency for the rate of convective flow to fall as said at least one seed crystal grows in size to occupy an ever-increasing proportion of the total autoclave cross-section, whereby said crystal grows at a substantially uniform rate.
 6. The method according to claim 5 wherein said heat applying step comprises: passing a first electrical current through at least one electrical heater disposed about the upper zone of said autoclave; and passing a second electrical current through at least one electrical heater disposed about the lower zone of said autoclave.
 7. The method according to claim 6 wherein said selective temperature differential increasing step comprises: altering the current supplied to at least one of said electrical heaters according to an empirically derived equation descriptive of the manner in which the temperatures of the upper and lower zones of the autoclave change, as a function of a change in the corresponding heater current, the equation being of the form d/dt ( y(t + Tau )) + Ay(t + Tau ) Bx(t) + C + N where, y(t + Tau ) the temperature of the corresponding zone at the instant t + Tau ; Tau the transport delay; N the stochastic noise term; A the time constant of the system; B/A the steady-state differential gain; and C/A the steady-state temperature of the corresponding autoclave zone when the heater current supplied thereto is zero.
 8. The method according to claim 5 wherein said crystal comprises quartz.
 9. In a hydrothermal crystal-growing process of the type wherein synthetic crystals are grown in an autoclave, a method of selectively controlling the rate of crystal growth comprising the steps of: computing, by machine means, the magnitude of the current supplied to heating means associated with the lower zone of said autoclave; computing, by machine means, the magnitude of the current supplied to heating means associated with the upper zone of said autoclave; and computing, by machine means, and by reference to a mathematical model descriptive of the physical behavior of said autoclave, incremental changes to said currents supplied to the heating means associated with the upper and lower zones of the autoclAve, said equation being of the form d/dt ( y(t + Tau )) + Ay(t + Tau ) Bx(t) + C + N where y(t + Tau ) the temperature of the corresponding zone at the instant t + Tau ; Tau the transport delay; N the stochastic noise term; A the time constant of the system; B/A the steady-state differential gain; C/A the steady-state temperature of the corresponding autoclave zone when the current supplied to the heating means is zero, whereby the growth rate of said synthetic crystals is selectively controlled.
 10. The process according to claim 9 including the further steps of: continuously sampling selected physical parameters within said autoclave; and computing, by machine means, updated values for the parameters of said mathematical model, based upon said sampled physical parameters.
 11. The process according to claim 10 wherein said selected physical parameters include at least the temperature of the upper and lower zones of said autoclave and the pressure developed therein.
 12. A method of controlling the rate of growth of a synthetic crystal grown from a seed crystal suspended in a nutrient solution within a substantially vertically disposed autoclave, comprising the step of: selectively altering the temperature gradient within said autoclave, as time proceeds to alter the rate of flow of nutrient solution over said seed crystal.
 13. A method of maintaining substantially constant the rate of growth of a quartz crystal which is grown from a seed crystal suspended in a nutrient solution of solvated quartz within a substantially vertically disposed autoclave, comprising the step of: selectively increasing the temperature gradient within said autoclave as time proceeds, to increase the convective rate of flow of solvated quartz over said seed crystal, to thereby offset the natural tendency for said rate to fall, as said seed crystal expands in size to occupy an ever-increasing proportion of the effective autoclave cross section.
 14. Apparatus for hydrothermally growing synthetic crystals comprising: a substantially vertically disposed autoclave, functionally divided into an upper zone and a lower zone, said autoclave being adapted to receive a charge of crystal-growing nutrient in the lower zone and of being substantially filled with a solvent capable of dissolving said nutrient; means for suspending at least one seed crystal within said autoclave, proximate the upper zone thereof; first and second heating means associated with said upper and lower autoclave zones, respectively; a source of energy for said first and second heating means; and computer means for respectively adjusting the amount of energy supplied to said first and second heating means from said source, said computer means including program means descriptive of the manner in which the temperatures of the upper and lower zones of said autoclave change, as a function of a change in the corresponding heater current supplied to said first and second heating means, said program means including an equation of the form d/dt( y(t Tau )) 30 Ay(t + Tau ) Bx(t) + C + N where y(t + Tau ) the temperature of the corresponding zone at the instant t + Tau ; Tau the transport delay; N the stochastic noise term; A the time constant of the system; B/A the steady-state differential gain; C/A the steady-state temperature of the corresponding autoclave zone when the current supplied to the heating means is zero, whereby the temperature differential between said upper and lower autoclave zones may be selectively altered during the crystal growing process.
 15. Apparatus according to claim 14 wherein said computer means is programmed to include a mathematical model descriptive of the thermodynamic behavior of said autoclave, and said apparatus further comprises: sensing means, coupled to said autoclave, for forwarding to said computing means information relative to the temperatures and pressure within said autoclave, whereby the parameters of said mathematical model may be adaptively altered as time proceeds.
 16. Apparatus according to claim 14 wherein: said first and second heating means each comprises at least one electrically operated heating element; said source of energy comprises a source of electrical energy, and said computing means comprises: a digital computer including at least a central processing unit, a memory storage device, a control circuit, a clock circuit, and input and output control circuits; and first and second magnetic amplifiers respectively interposed between said source of electrical energy and said electrically operated heating elements, said first and second magnetic amplifiers being coupled to said output control circuit, whereby signals representative of the currents that it is desired to feed to said heating elements are forwarded by said digital computer to said magnetic amplifiers to control the gain thereof and hence the currents fed to said heating elements.
 17. Apparatus according to claim 14 wherein: said first and second heating means each comprise at least one electrically operated heating element; said source of energy comprises a source of electrical energy, and said computing means comprises: a digital computer including at least a central processing unit, a memory storage device, a control circuit, a clock circuit, and input and output control circuits; and first and second silicon control rectifier circuits respectively interposed between said source of electrical energy and said electrically operated heating elements, said first and second silicon control rectifier circuits being coupled to said output control circuit, whereby signals representative of the currents that it is desired to feed to said heating elements are forwarded to the control elements of said silicon control rectifier circuits by said digital computer to control the duty cycle thereof and hence the currents fed to said heating elements.
 18. Apparatus for hydrothermally growing synthetic quartz crystals exhibiting substantially uniform mechanical Q throughout all crystallographic regions thereof, which comprises: a substantially vertically disposed autoclave, functionally divided into an upper and lower zone, said autoclave being adapted to receive a charge of crushed quartz in the lower zone thereof and a solution capable of dissolving said charge in both said upper and lower zones; means for suspending at least one quartz seed crystal within said autoclave, proximate the upper zone thereof; first and second electrically operated heating elements respectively associated with said upper and lower zones; a source of electrical energy for said first and second heating elements; and a digital computer for respectively adjusting the amount of energy fed from said source to said first and second heating elements, said digital computer including program means descriptive of the manner in which the temperatures of the upper and lower zones of said autoclave change, as a function of a change in the corresponding heater current supplied to said first and second heating means, said program means including an equation of the form d/dt( y(t + Tau )) + Ay(t + Tau ) Bx(t) + C + N where y(t + Tau ) the temperature of the corresponding zone at the instant t + Tau ; Tau the transport delay; N the stochastic noise term; A the time constant of the system; B/A the steady-state differential gain; C/A the steady-state temperature of the corresponding autoclave zone when the current supplied to the heating means is zero, whereby the temperature differential established within said autoclave between the upper and lower zones thereof is selectively altered during the crystal-growing process to correspondingly increase the rate of flow of solvated quartz over said seed crystal, thereby maintaining a substantially constant rate of crystal growth.
 19. Apparatus according to claim 18 wherein said digital computer includes a memory storage device priorly programmed to include a mathematical model descriptive of the thermodynamic behavior of said autoclave to step changes in the heater currents supplied to the heating elements associated with said upper and lower zones, said memory storage device having further been priorly programmed to include the temperature profile that it is desired said upper and lower autoclave zones should attain, as time proceeds, said apparatus further comprising: first and second temperature sensing devices respectively coupled to the upper and lower zones of said autoclave; and a pressure sensing device for sensing the pressure developed within said autoclave, said temperature sensing devices and said pressure sensing devices being connected to said digital computer, said digital computer selecting, on the basis of the temperature and pressure information fed thereto, the appropriate parameters for said mathematical model, and thereafter periodically computing the currents which are to be fed to said heating elements, so that the temperatures of the upper and lower zones of said autoclave approach the temperatures dictated by said priorly stored temperature profile, to within a given limit of error.
 20. Apparatus according to claim 19 wherein said digital computer includes at least a central processing unit, a clock circuit, a control circuit and a process control input circuit and a process control output circuit, said apparatus further comprising: means, connected to said process control output circuit, for controlling the current supplied from said electrical energy source to said heating elements, in accordance with signals received from said computer, said temperature sensing devices and said pressure sensing device being connected to said digital computer through said process control input circuit.
 21. The apparatus according to claim 26 wherein said current controlling means comprises first and second magnetic amplifiers respectively associated with the heating elements associated with the upper and lower zones of said autoclave.
 22. The apparatus according to claim 20 wherein said current controlling means comprises first and second silicon control rectifier circuits respectively associated with the heating elements associated with the upper and lower zones of said autoclave.
 23. The apparatus according to claim 20, further comprising: first and second digital-to-analog converter circuits interposed between said process control output circuit and said current controlling means; and first, second and third analog-to-digital converter circuits interposed between said temperature sensors and said pressure sensor and said process control input circuit.
 24. A method of controlling, by computer, a hydrothermal crystal-growing process, of the type wherein synthetic crystals are grown in an autoclave functionally divided into upper and lower zones and having electrically operated heating elements associated therewith, said crystal-growing process being divided into at least a warm-up phase and a run phase, said warm-up phase being subdivided into at least three regions, the method comprising the steps of: loading into the memory area of said computer an empirically-derived mathematical model descriptive of the behavior of said autoclave in respect to step changes in the currents supplied to the heater elements associated with said upper and lower zones of the autoclave; loadIng into the memory area of said computer the temperature profile that it is desired said upper and lower autoclave zones should attain, during said run phase; continuously sampling, by machine means, at least the upper and lower zone temperatures of said autoclave; determining, by machine means, from said temperature samples, whether said autoclave is operating in the run phase or in the warm-up phase; selecting, by machine means, the appropriate values for the parameters of said mathematical model, according to the phase and/or phase region said autoclave is operating in, the sampled temperatures, and the elapsed time; computing, by machine means, and by reference to said mathematical model, the currents which should be fed to the heating elements associated with the upper and lower zones of said autoclave, in order that said zones attain the temperatures required by said profile; and then feeding said computed currents to the heating elements associated with said upper and lower autoclave zones, whereby the temperatures of said upper and lower zones approach the desired temperatures dictated by the stored temperature profile, to within a given degree of error.
 25. A method of controlling, by computer, a hydrothermal crystal growing process, of the type wherein synthetic crystals are grown in an autoclave functionally divided into upper and lower zones and having electrically operated heating elements associated therewith, said crystal-growing process being divided into at least a warm-up phase and a run phase, the method comprising the steps of: loading into the memory area of said computer an empirically-derived mathematical model descriptive of the behavior of said autoclave in respect to step changes in the currents supplied to the heater elements associated with said upper and lower zones of the autoclave, said model being of the form d/dt( y(t + Tau )) + Ay(t + Tau ) Bx (t) + C + N where y(t + Tau ) the temperature of the corresponding zone at the instant t + Tau ; Tau the transport delay; N the stochastic noise term; A the time constant of the system; B/A the steady-state differential gain; C/A the steady-state temperature of the corresponding autoclave zone when the heater current supplied thereto is zero; loading into the memory area of said computer the temperature profile that it is desired said upper and lower autoclave zones should attain, during said run phase; continuously sampling, by machine means, at least the upper and lower zone temperatures of said autoclave; determining, by machine means, from said temperature samples, whether said autoclave is operating in the run phase or in the warm-up phase; selecting, by machine means, the appropriate values for the parameters of said mathematical model, according to the phase said autoclave is operating in, the sampled temperatures, and the elapsed time; computing, by machine means, and by reference to said mathematical model, the currents which should be fed to the heating elements associated with the upper and lower zones of said autoclave, in order that said zones attain the temperatures required by said profile; and then feeding said computed currents to the heating elements associated with said upper and lower autoclave zones, whereby the temperatures of said upper and lower zones approach the desired temperatures dictated by the stored temperature profile, to within a given degree of error. 